This article focuses on estimating rare events using multilevel splitting schemes. The event of interest is that a Markov
process enters some rare set before another ("tabu") set. It is known that in this setting a large deviations analysis is
not always sufficient for constructing asymptotically efficient importance sampling schemes; additional modifications to the
change of measure suggested by large deviations are needed. As an alternative, we design an asymptotically efficient multilevel
splitting scheme that relies on the large deviations analysis only. This property makes it more flexible and easier to implement
than corresponding importance sampling schemes.

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